# Simple Length Rigidity for Hitchin Representations

## TL;DR

This paper demonstrates that Hitchin representations are uniquely identified by spectral radii of simple, non-separating curves, and classifies isometries of the intersection function on Hitchin components, using a transversality result for positive quadruples of flags.

## Contribution

It introduces a spectral characterization of Hitchin representations and classifies isometries of the intersection function, advancing understanding of Hitchin components.

## Key findings

- Hitchin representations are determined by spectral radii of certain curves.
- Classification of isometries of the intersection function on Hitchin components.
- Establishment of a transversality result for positive quadruples of flags.

## Abstract

We show that a Hitchin representation is determined by the spectral radii of the images of simple, non-separating closed curves. As a consequence, we classify isometries of the intersection function on Hitchin components of dimension 3 and on the self-dual Hitchin components in all dimensions. As an important tool in the proof, we establish a transversality result for positive quadruples of flags.